Finding the Derivative of an Integral: Explanation Needed

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The discussion revolves around finding the derivative of an integral involving the equation u(1/r)((d/dr)[(r)(dV/dr)])=P. A user struggles with their initial integration attempt, which led to an incorrect result for V, and seeks clarification on the correct answer, which includes additional terms. The importance of including constants during integration is highlighted as a potential reason for the discrepancy in results. The conversation also touches on the proper application of differentiation under the integral sign. Overall, the thread emphasizes the need for careful integration techniques to achieve the correct solution.
juice34
1. Homework Statement
Can someone help me take the derivative of the integral
u(1/r)((d/dr)[(r)(dV/dr)])=P


2. Homework Equations



3. The Attempt at a Solution
my attempt yields V=(Pr^2)/(2u)+C(1), which is not right. The actual answer is V=(Pr^2)/4u+C(1)ln(r)+C(2). I am having trouble finding out where the 4 and everything else comes from could someone please explain to me what is going on. Thank YOU
 
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When you first integrated, did you include your constant? If not, that might explain why you lacked the extra term upon the second integration.
 
You want to find
\frac{d}{dx}\int u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}dr?
That, of course, is equal to
u(1/r)\frac{d\left(r\frac{dV}{dr}\right)}{dr}?

Or do you mean the integral of that integral?
 

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